Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2008, No.1

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Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.-Math. Sci., 2008, No.1

Proceedings of the National Academy of Sciences of Belarus
(Vestsi Natsiyanalnai Akademii Navuk Belarusi)
SERIES OF PHYSICAL-MATHEMATICAL SCIENCES
Published by Belaruskaya Navuka Publishing House, Minsk, Republic of Belarus

Number 1, 2008

MATHEMATICS

Roudenok A. E.
Strongly isochronous center and the focus of the system with third-degree polynomials. pp. 4--12

Summary: Formulas for computing necessary and sufficient conditions of strongly isochronous centers and focus of the system with third-degree polynomials are obtained. Examples of the strongly isochronous centers and focus are given.

Laptinsky V. N.
Problem on the half-axis-limited solutions of nonlinear differential systems. pp. 13--15

Summary: A method to construct limited solutions for the nonlinear differential systems is developed.

Strylets M. M.
One completely regularized non-local quasi-Newton method for solution of nonlinear problems. pp. 16--22

Summary: The non-local superlinear quasi-Newton iterative method for solution of the nonlinear equations f(x) = 0 in a Hilbert space is considered. The given method allows one to avoid situations, when at a reversion of a derivative of Frechet f '(x) on some iteration of the process in zero a converging sequence of approximations turns out, but its limit is not a solution of the considered equation. It is reached due to a complete regularization of the linear system solved on each step of the iterative method. Convergence of the obtained process is researched at various limitations on smoothness of an operator f. Effectiveness of the offered method is analyzed by a test example.

Egorov A. D.
Approximate evaluation of functional integrals based on a connection between Wiener and Poisson spaces. pp. 23--27

Summary: An approximate formula for evaluation of functional integrals with an integrand depending on jump times of the Poisson process is constructed. The formula is based on a connection between distributions of jump times of the Poisson process and the half sum of the squares of two independent linear Wiener functionals. The error of the composed approximate formula is estimated.

Rjabchenko A. I.
Partially saturated formation with X^w-defect 1. pp. 28--34

Summary: Let X be a 2-multiply saturated formation. In this article we describe an w-saturated formation of finite groups with X^w-defect 1.

Zhuk E. E.
Projection of the multivariate probability mixtures with a partial keeping of the interclass distances. pp. 35--40

Summary: The problem on the projection of observations in multivariate statistical classification is considered. The special transformation of the initial feature space to the space with a less dimension which partially keeps the Mahalanobis interclass distances is proposed.

Monastyrnyi P. I., Kremen E. V., Kremen Yu. A.
Numerical solution of the three-point grid equations when combining the reduction method and the conjugate gradient method. pp. 41--44

Summary: A new method of solving grid boundary-value problems with separate boundary conditions is constructed and justified. The main idea of this method consists in constructing the two-stage structure of a computational algorithm. Combining the reduction method and the conjugate gradient method has formed the basis for this new method.

Kovalevskaya E. I., Morozova I. M.
Inhomogeneous Diophantine approximations for the points of the square and cubic parabolas in the ring of adeles. pp. 45--48

Summary: We prove an analogue of the convergence part of the Khintchine-type theorem on inhomogeneous Diophantine approximations for the points of the square and cubic parabolas in the ring of adeles. This expands the previons results of the authors.

Erofeenko V. T., Tavakkoli D. P.
Models of the boundary conditions in electrodynamics on screens and shells with distributed inhomogeneities. pp. 49--55

Summary: Different kinds of the conjugate boundary conditions for electromagnetic fields on thin laminate shells and the impedance boundary conditions on conducting bodies with composite coatings were examined.

PHYSICS

Zhestkov S. V.
Soliton-like solutions of the Klein--Gordon equation with the Kerr nonlinearity. pp. 56--59

Summary: Some exact soliton-like solutions of the Klein--Gordon equation with the Kerr nonlinearity are presented.

Andrushkevich I. E.
Matrix presentation of the Maxwell equation in inhomogeneous isotropic media. pp. 60--66

Summary: This article deals with the matrix way in the presentation of the system of Maxwell equations. The Clifford algebra of elementary matrices has been studied. They allow one to present the Maxwell equations in the way analogous to Dirac's relativistic wave equation. The results achieved allow using the well-developed algebraic method of differentiation of variable quantities when investigating the Maxwell equations.

Baryshevsky V. G., Rouba A. A.
Birefringence and spin dichroism for deuterons with an energy of 50--20 MeV. pp. 67--73

Summary: The obtained results confirm that birefringence and spin dichroism of deuterons can be observed experimentally. For compensating energy loss and increasing effects a storage ring and an internal gas target can be used.

Degtyareva E. A., Timoshin S. I.
Semi-inclusive deep inelastic scattering (anti)neutrino on polarized targets. pp. 74--79

Summary: Asymmetries for the semi-inclusive deep inelastic scattering (anti)neutrino on polarized targets with a charged weak current have been obtained for the case of p-mesons production. It was obtained in the terms of the quark-parton model and in the Born approach. These asymmetries do not depend on the functions of fragmentation of p-mesons. The contributions of quark flavours and valency quarks to the spin of nucleon have been determined.

Pletyukhov V. A., Strazhev V. I.
Massive gauge invariant theories and massless fields. pp. 80--88

Summary: Different massless and massive gauge invariant fields within the framework of the theory of generalized relativistic wave equations are considered.

Korshunov F. P., Gurinovich V. A., Karas V. I.
Annealing of radiation defects in unalloyed arsenicum gallium of n-type, doped with hydrogen. pp. 89--91

Summary: The annealing of radiation defects in unalloyed arsenicum gallium of n-type, doped with hydrogen and irradiated with 4-MeV fast electrons has been investigated. Two stages of the annealing of the radiation defects have been found. It has been determined that the annealing activation energy of the radiation defects is equal to 0,50 ± 0,05 eV at the first annealing stage and 1,55 ± 0,10 eV at the second annealing stage.

Akimov A. I., Sauchuk G. K., Sauchuk V. A., Letko A. K.
Electrophysical properties of the ceramic materials in the Bi₂Ti₂O₇ -- TiO₂ system. pp. 92--96

Summary: Dielectric properties of ceramic materials of a binary Bi₂Ti₂O₇ -- TiO₂ system are studied. The influence of doped Sn²⁺, Mn²⁺, Gd³⁺, Eu³⁺ on the increase of dielectric parameters of the ceramic samples, which were obtaind on the base of the Bi₂Ti₂O₇ -- TiO₂ system specimens are studied. The results of the dielectric investigations of the ceramic doped specimens of Bi₂Ti₂O₇ -- TiO₂ are investigated. The results of the dielectric parameters temperatures measured in the range of (0--300) °C are presented. The perspective of using ceramics of the modified Bi₂Ti₂O₇ -- TiO₂ system for creating the potential for use in the functional components of microwave devices on its base is shown.

Hryharyshyn I. L., Kudanovich A. M., Dziomin V. S., Krasouski A. N., Pakatashkin V. I.
Research of the characteristics of a thin-film semiconductor ozone sensor based on nickel oxide. pp. 97--101

Summary: A semiconductor gas sensor on the basis of thin-film nickel oxide has been examined in the article. The sensor scheme and the experimental set-up for ozone-sensitive feature research are described. The characteristics of the sensor in a wide range of ozone concentrations at different values of its active element have been studied thoroughly. The result is the NiO-based sensor can be used as an ozone-sensitive element of a device for atmosphere ozone concentration indication.

INFORMATICS

Likhoded N. A.
Generalized parallelepiped method for parallelization of cycles. pp. 102--107

Summary: Sufficient conditions for partition of nested loops on independent parts are suggested and proved. Algorithms to obtain parallel sets of operations are developed.

Evdokimovich V. E., Starovoitov A. N.
Stationary distribution of multimode service policy networks with arbitrary distributions of the servicing and switching time. pp. 108--114

Summary: We consider open and closed preemptive-resume queuing systems with symmetrical disciplines of the service. Single-server nodes have several service modes (regimes); the amount of work required for switching between the modes is a random variable with an arbitrary distribution function. Switching can be made to adjacent modes only. The amount of work required for servicing an incoming customer (workload) is also a random variable with an arbitrary distribution function. For an open network, the input flow is the Poisson one. We prove that the stationary distribution of the network states is invariant with respect to a functional form of workload and switching regime distributions if the first moments are fixed.

SCIENTISTS OF BELARUS

Andrei Markovich Goncharenko (To the 75^th Birthday Anniversary). pp. 115--116
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Aleksandr Pavlovich Voitovich (To the 70^th Birthday Anniversary). pp. 117--119
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Konstantin Nikolaevich Soloviev (To the 75^th Birthday Anniversary). pp. 120--121
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Valentin Vladimirovich Muraviev (To the 70^th Birthday Anniversary). pp. 122--123
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